Jim, if hiding the price / add to cart are the only differences, a separate template is not necessary - it just makes two things to maintain. You could instead use a tag on those products and add logic around the liquid code with the price/add to show only if not tagged with something like "HidePrice". If you are using tags as filters, you would have to further mod the code to not include in that functionality tags used for such purposes (e.g. skip tags for the filter functions that start with "int" for internal tag). Otherwise, 2 templates might make sense.
In any event, open your template in the theme editor (product.liquid or whatever you've called it) and search for produce.price. It will look like {{ product.price | money }} That is the code you will want to remove. Similar for the add-to-cart issue.